Gradient expansion of the non-Abelian gauge-covariant Moyal star-product
- URL: http://arxiv.org/abs/2111.01497v1
- Date: Tue, 2 Nov 2021 10:53:28 GMT
- Title: Gradient expansion of the non-Abelian gauge-covariant Moyal star-product
- Authors: Fran\c{c}ois Konschelle (CHU de Bordeaux)
- Abstract summary: Motivated by the recent developments of gauge-covariant methods in the phase-space, a systematic method is presented aiming at the generalisation of the Moyal star-product to a non-Abelian gauge covariant one at any order.
It might be of fundamental importance for the mathematical elaborations of gauge theory using the strict or deformation quantisation principles.
A gauge-covariant formulation taking into account possible geometrical connections in both the position and momentum spaces is also constructed at leading orders.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Motivated by the recent developments of gauge-covariant methods in the
phase-space, a systematic method is presented aiming at the generalisation of
the Moyal star-product to a non-Abelian gauge covariant one at any order. Such
an expansion contains some dressing of the bare particle model by the
gauge-fields explicitly, and might serve as a drastically simplifying tool for
the elaborations of gauge-covariant quantum transport models. In addition, it
might be of fundamental importance for the mathematical elaborations of gauge
theory using the strict or deformation quantisation principles. A few already
known examples of quantum kinetic theories are recovered without effort as an
illustration of the power of this tool. A gauge-covariant formulation taking
into account possible geometrical connections in both the position and momentum
spaces is also constructed at leading orders, with applications to the
generation of gauge-covariant effective theories in the phase-space. This paper
is devoted to the pedestrian elaboration of the gradient expansions. Their
numerous consequences will be explored in subsequent works.
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